Theoretical Calculation of Thermodynamic Properties of

compounds, method 2 has the smallest average absolute deviation from the experimental data. All values for the heat capacity, entropy, enthalpy, and e...
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J. Chem. Eng. Data 2003, 48, 727-735

727

Theoretical Calculation of Thermodynamic Properties of Polybrominated Dibenzo-p-dioxins Xian-Wei Li,* Etsuro Shibata, and Takashi Nakamura Institute of Multidisciplinary Research for Advanced Material, Tohoku University, 1,1 Katahira, 2-Chome, Aobaku, Sendai 980-8577, Japan

Heat capacities and entropies for 76 polybrominated dibenzo-p-dioxins (PBDDs) in the gas state at 298.15 K and 101.325 kPa have been computed using the density functional theory (B3LYP/6-31G(d)) with Gaussian 98. Based on the output data of Gaussian, three methods were employed to calculate enthalpies and Gibbs energies of formation of the 76 PBDDs in the gaseous state at 298.15 K and 101.325 kPa. To assess the three methods, thermodynamic properties of 16 compounds were first calculated by B3LYP/ 6-31G(d) and compared with reference values. For predicting the enthalpies of formation of the reference compounds, method 2 has the smallest average absolute deviation from the experimental data. All values for the heat capacity, entropy, enthalpy, and energy of formation of the 76 PBDDs increase as the number of substituted bromines increases. For isomers of tetrabromodibenzo-p-dioxins, 1,3,6,8-TeBDD, 1,3,7,8TeBDD, 1,3,7,9-TeBDD, and the most toxic compound 2,3,7,8-TeBDD are more stable than the others and easier to form during the formation process.

1. Introduction Polybrominated dibenzo-p-dioxins (PBDDs) and polybrominated dibenzofurans (PBDFs) can be formed by chemical, photochemical, or thermal reactions from precursors and by so-called de novo synthesis. PBDDs and PBDFs have been found as contaminants in brominated organic chemicals and, in particular, in flame retardants: polybrominated diphenyl ethers (PBDEs), decabromobiphenyl (decaBB or DBB), 1,2-bis(tribromophenoxy)ethane, tetrabromobisphenol A (TBBPA), and others. They have been detected in distillation residues of some bromophenols and bromoanilines and in wastes from chemical laboratories. Brominated flame retardants and their precursors appear to be a main source of PBDDs and PBDFs. As concluded by the World Health Organization (WHO), the potential of PBDDs and PBDFs for biological (e.g., enzyme induction) and toxic effects is similar to that of the polychlorodibenzo-p-dioxins (PCDDs) and polychlorodibenzofurans (PCDFs). PBDDs and PBDFs are contaminants that are more or less similar to PCDDs and PCDFs in their persistence and toxicity.1 There is much less information on PBDDs and PBDFs than on their chlorinated analogues, and there are very few experimental data on their physical and chemical properties. The analytical methods for separating and identifying the individual brominated congeners are much less advanced than those for their chlorinated analogues, and only few reference standards are available. Current analytical methods are able to quantify total brominated homologue groups and also to detect but not quantify the mixed brominated/chlorinated congeners. Because of the complexity of analytical procedures, it has been possible to characterize and determine only a small number of PBDD/Fs and PXDD/Fs, and only a few of the compounds have CAS registry numbers. In this study, the thermodynamic properties (heat capacity, entropy, and Gibbs energy of formation) in the gaseous * Corresponding author. Telephone: 81-22-217-5214. Fax: 81-22-2175214. E-mail: [email protected].

state at 298.15 K and 101.325 kPa were computed for all 76 PBDDs using density functional theory (DFT) with Gaussian 98 programs.2 The purpose of the study was to obtain a consistent set of thermodynamic values for PBDDs. The discrepancy between the calculated results and available experimental values for 16 compounds (brominated arenes) is also discussed. The present thermodynamic data are, to our knowledge, the first set of calculated data reported on PBDDs. 2. Computational Methods Becke’s three-parameter hybrid functional combined with the gradient-correlation functional of Lee, Yang, and Parr (LYP), denoted B3LYP, was employed in the computations using DFT. The all-electron 6-31G(d) basis set was employed. Geometries were optimized using analytic gradient techniques, that is, the Berny algorithm with redundant internal coordinates. The stationary points on the potential energy surface were characterized by calculations of vibrational frequencies, which were done analytically at DFT levels. Following the geometry optimization, frequencies were calculated using the same method at a stationary point. The zero-point vibrational energies (ZPE) calculated at the DFT level were scaled by 0.9804.3 Throughout this paper, all calculations for PBDDs were carried out with B3LYP/6-31G(d) Opt Freq. This computational model level is different from those which have been applied to calculate the thermodynamic values of dioxin congeners serially.4-6 The equations used for computing thermochemical data in Gaussian programs are derived from statistical thermodynamics. Two key ideas of statistical thermodynamics are the Boltzmann distribution and the partition function. The partition function is like a thermodynamic wave function, in the sense that it contains all thermodynamic information about the system, just as the quantum mechanical wave function contains all dynamic information. 2.1. Entropy and Heat Capacity. The entropy and heat capacity can be directly obtained from the output of

10.1021/je0256582 CCC: $25.00 © 2003 American Chemical Society Published on Web 04/15/2003

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Journal of Chemical and Engineering Data, Vol. 48, No. 3, 2003

Table 1. Enthalpies of Formation for Gaseous Atoms and Entropy and (H298K - H0K) Values for Elements in Their Reference State from Experimentsa atoms

state

∆fH°(0K)/kJ‚mol-1

∆fH°(298K)/kJ‚mol-1

state

S°(298K)/J‚mol-1‚K-1

H298K - H0K/kJ‚mol-1

C H Br O N

gas gas gas gas gas

711.19 ( 0.46 216.035 ( 0.006 117.92 ( 0.06 246.79 ( 0.10 470.82 ( 0.10

716.67 ( 0.46 217.999 ( 0.006 111.86 ( 0.06 249.17 ( 0.10 472.68 ( 0.10

reference state reference state reference state reference state reference state

5.74 ( 0.21 65.340 ( 0.017 76.103 102.574 ( 0.018 95.805 ( 0.010

1.051 4.238 12.255 4.342 4.335

a

Chase, 1998 (ref 15).

Gaussian programs. The equations used for computing thermochemical data in the programs are equivalent to those given in statistical mechanics texts.7,8 2.2. Enthalpy and Gibbs Energy of Formation. The following equations are employed to calculate the absolute internal energy (U), enthalpy (H), and Gibbs energy (G) of the molecule at zero Kelvin and the specified temperature (T):7-9

U0K ) Eelec + Ezpe

(1)

UT ) U0K + (Etrans + Erot + Evib)T

(2)

HT ) UT + RT

(3)

GT ) HT - TS

(4)

where Eelec is the internal energy due to electronic motion and Ezpe the zero point energy of the molecule at 0 K (a correction to the electronic energy). Etrans, Erot, and Evib are the thermal energy corrections due to the effects of molecular translation, rotation, and vibration at the specified temperature, respectively. In this study, Eelec is computed at the B3LYP level. Etrans, Erot, and Evib can be rapidly calculated using statistical thermodynamics. All the values of Eelec, Ezpe, UT, HT, and GT are given in hartrees (atomic units, 1 hartree ) 2625.51 kJ‚mol-1) by the output of the program. On the basis of these absolute energy values, enthalpy and Gibbs energy of formation can be calculated by different methods. 2.2.1. Method 1. The enthalpies of formation at 0 K were calculated by subtracting the calculated atomization energies (∑D0) from the known enthalpies of formation of the isolated atoms. The enthalpies of formation at 298.15 K were calculated by correction to the enthalpies of formation at 0 K. This method is the common theoretical method for calculating the enthalpy of formation used by many studies.6,9-11 For the computation of enthalpies of formation, Curtiss et al.11 tested seven density functional methods: B3LYP, BP86, B3P86, BPW91, B3PW91, and SVWN with 148 molecules. Of these seven DFT methods, the B3LYP method has the smallest average absolute deviation (13.0 kJ‚mol-1) from the experimental values. The calculation procedure is as follows:

∑ x∆ H°(X,0K) - ∑ D (M) ) ∑ x∆ H°(X,0K) - [∑ xU(X,0K) - U(M,0K)]

∆fH°(M,0K) )

f

0

f

(5)

∆fH°(M,298K) ) ∆fH°(M,0K) + [H°(M,298K) H°(M,0K)] -

∑ x(H

298K

- H0K)X (6)

∆fG°(M,298K) ) ∆fH°(M,298K) - T∆S ) ∆fH°(M,298K) - T[S°(M,298K) -

∑ xS°(X,298K)]

(7)

where ∆fH° and ∆fG° are the standard-state enthalpy and Gibbs energy of formation of the ideal gas, respectively. M stands for the molecule of the compound, X identifies each element which composes M, and x is the stoichiometric

coefficient of the constituent. (H298K - H0K)X is the formation enthalpy correction from 0 K to 298 K for elements in the reference state. Dixon et al.12,13 have used high-level ab initio electronic structure theory to calculate the heats of formation of CBr, CHBr, CBr2, and other small halogenated compounds. It was found that the spin-orbit corrections must be applied to the atomization energies of these compounds, especially brominated compounds, as the atomic energies are calculated incorrectly without spin-orbit corrections. An atomic spin-orbit correction of -3.51 kcal‚mol-1 (-14.69 kJ‚mol-1) for Br on the basis of the excitation energy tables of Moore14 was proposed. The spin-orbit correction ∆ESO of -14.69 kJ‚mol-1 per Br atom was applied to the calculations of atomization energy (∑D0) in this study. ∆fH°(X), S°(X,298 K), and (H298K - H0K)X are tabulated in Table 1, cited from the NIST-JANAF Thermochemical Tables.15 The absolute standard-state entropy S°(X,298 K) used for elemental carbon, hydrogen, bromine, and oxygen (reference state) should be (5.740, 130.680/2, 152.206/2, and 205.147/2) J‚mol-1‚K-1, respectively, not the values cited in Ochterski’s paper9 (not in the reference state). The calculated thermochemistry values using B3LYP/ 6-31G(d) for C, H, Br, O, H2, Br2, CH4, CH3Br, C6H6, C6H5Br, dibenzo-p-dioxin (DD), and 2,3,7,8-tetrabromodibenzop-dioxin (TBDD) are listed in Table 2; all values are in hartrees. Method 1 is illustrated with the example calculations for bromomethane and TBDD as follows: For bromomethane (CH3Br),

∑D (CH Br) ) {[1 × U(C,0K) + 3 × U(H,0K) + 1 × 0

3

U(Br,0K)] - U(CH3Br,0K)} + 1 × ∆ESO ) {[1 × (-37.846280) + 3 × (-0.500273) + 1 × (-2571.656918)] - (-2611.579925)} × 2625.51 + 1 ×

(-14.69) ) 1497.4 kJ‚mol-1 ∆fH°(CH3Br,0K) ) [1 × ∆fH°(C,0K) + 3 ×

∑

∆fH°(H,0K) + 1 × ∆fH°(Br,0K)] - D0(CH3Br) ) (1 × 711.19 + 3 × 216.035 + 1 × 117.92) - 1497.4 ) -20.2 kJ‚mol-1 ∆fH°(CH3Br,298K) ) ∆fH°(CH3Br,0K) + [H°(CH3Br,298K) - H°(CH3Br,0K)] - [1 × (H298K H0K)C + 3 × (H298K - H0K)H + 1 × (H298K - H0K)Br] ) (-20.2) + [(-2611.575866) - (-2611.579925)] × 2625.51 - (1 × 1.051 + 3 × 4.238 + 1 × 12.255) ) -35.6 kJ‚mol-1 ∆fG°(CH3Br,298K) ) ∆fH°(CH3Br,298K) - 298.15 × [S°(CH3Br,298K) - 1 × S°(C,298K) - 3 × S°(H,298K) - 1 × S°(Br,298K)] ) (-35.6) - 298.15 × (255.191 - 1 × 5.740 - 3 × 65.340 - 1 × 76.103)/1000 ) -28.8 kJ‚mol-1

Journal of Chemical and Engineering Data, Vol. 48, No. 3, 2003 729 Table 2. Calculated Thermochemistry Values in the Gas Phase at 101.325 kPa by B3LYP/6-31G(d) (hartrees) substance

U0K ()H0K)a

U298Kb

H298Kb

G298Kb

C H Br O H2 Br2 CH4 CH3Br C6H6 C6H5Br DD TBDD

-37.846 280 -0.500 273 -2 571.656 918 -75.060 623 -1.165 536 -5 143.398 381 -40.474 045 -2 611.579 925 -232.149 871 -2 803.264 629 -612.362 477 -10 896.808 498

-37.844 864 -0.498 857 -2 571.655 502 -75.059 207 -1.163 175 -5 143.395 626 -40.471 177 -2 611.576 811 -232.145 411 -2 803.258 848 -612.352 659 -10 896.792 547

-37.843 920 -0.497 913 -2 571.654 558 -75.058 263 -1.162 231 -5 143.394 682 -40.470 233 -2 611.575 866 -232.144 467 -2 803.257 904 -612.351 714 -10 896.791 602

-37.860 825 -0.510 927 -2 571.673 748 -75.075 575 -1.177 023 -5 143.422 540 -40.493 715 -2 611.604 846 -232.175 017 -2 803.294 903 -612.398 258 -10 896.856 484

a U b 0K and H0K are the absolute internal energy and enthalpy of the molecule at 0 K. U298K, H298K, and G298K are the absolute internal energy, enthalpy, and Gibbs energy of the molecule at 298.15 K, respectively (1 hartree ) 2625.51 kJ‚mol-1).

For TBDD (C12H4Br4O2),

∆fH°(TBDD,0K) ) [12 × ∆fH°(C,0K) + 4 × ∆fH°(H,0K) + 4 × ∆fH°(Br,0K) + 2 × ∆fH°(O,0K)] {12 × U(C,0K) + 4 × U(H,0K) + 4 × U(Br,0K) + 2 × U(O,0K) - U(TBDD,0K) + 4 × ∆ESO} ) (12 × 711.185 + 4 × 216.035 + 4 × 117.917 + 2 × 246.790) - {[12 × (-37.846280) + 4 × (-0.500273) + 4 × (-2571.656918) + 2 × (-75.060623) (-10896.808498)] × 2625.51 + 4 × (-14.69)} ) 174.7 kJ‚mol-1 ∆fH°(TBDD,298K) ) ∆fH°(TBDD,0K) + [H(TBDD,298K) - H(TBDD,0K)] - [12 × (H298K H0K)C + 4 × (H298K - H0K)H + 4 × (H298K - H0K)Br + 2 × (H298K - H0K)O] ) 174.7 + [(-10896.791602) (-10896.808498)] × 2625.51 - (12 × 1.051 + 4 ×

calculated from the three reactions shown in Chart 1 (all reactants and products are in the gas state). The average values of enthalpy and Gibbs energy of formation of TBDD calculated from reactions I, II, and III are 64.3 kJ‚mol-1 and 144.4 kJ‚mol-1, respectively. 2.2.3. Method 3 (Benson’s Method). The third method for estimating the enthalpies of formation is consistent with the group additivity technique developed by Benson.20 It is a traditional empirical method. Benson group values have been substantially refined during the years; for example, the CHETAH program21 by ASTM International predicts thermochemical properties using a modern Benson application. The available values of group contributions to the enthalpy of formation given by CHETAH 7.3 are listed in Table 3. For TBDD,

∆fH°TBDD ) 4(CbH) + 4(CbBr) + 4[Cb-(O)] + 2[O-(Cb)2] + ∆ring + 2∆ortho ) 4 × 13.807 + 4 × 44.769 + 4 × (-3.766) + 2 × (-78.659) + 8.368 + 2 × 3.138 ) 76.6 kJ‚mol-1

4.238 + 4 × 12.255 + 2 × 4.342) ) 131.8 kJ‚mol-1 2.2.2. Method 2. Using B3LYP/6-31G(d), it was found that the enthalpy of formation results for benzene and DD calculated by method 1 differ greatly from the experimental data. Therefore, a simple method, method 2, was proposed here. Because the absolute enthalpy (H) and Gibbs energy (G) values of the molecule can be obtained through theoretical calculation, it is easy to obtain the reaction enthalpy and Gibbs energy for any reaction using these energy values by eqs 8 and 10. In another way, the reaction enthalpy and Gibbs energy can be calculated by eqs 9 and 11, respectively.

∆rH°(298K) )

∑(H

∆rH°(298K) ) ∆rG°(298K) )

298K)products

∑(H

∑(∆ H° f

298K)products

∑(G

∆rG°(298K) )

-

298K)products

∑(∆ G° f

-

-

298K)reactants

∑(∆ H° f

298K)reactants

∑(G

298K)products

298K)reactants

-

∑(∆ G° f

(8)

(9) (10)

298K)reactants

(11)

Combining these equations and using the experimental data of enthalpy and Gibbs energy of formation for H2, Br2, CH4, CH3Br, C6H6, C6H5Br, and DD,15-19 the unknown enthalpy and Gibbs energy of formation of TBDD can be

3. Results and Discussion To assess the accuracy of the three methods used to predict the enthalpy and Gibbs energy of formation, the thermodynamic properties of 16 compounds (brominated arenes) were first calculated and compared with available experimental data. 3.1. Discrepancy Analysis for the Computation of Thermodynamics. For brominated arenes, in fact, only minimal experimental thermodynamic data are available. Table 4 shows the calculation results of U, G, H, S, Cp, ∆fH, and ∆fG for benzene, bromobenzenes, benzoic acid, bromobenzoic acids, naphthalene, and bromonaphthalenes in the standard-state ideal gas at 298.15 K and 101.325 kPa. As shown, the calculated results of heat capacity and absolute entropy are in good agreement with experimental data, although few such data are available. On the properties of heat capacity and absolute entropy, the calculation results obtained by B3LYP/6-31G(d) seem to be accurate, since Gaussian employs the mature theoretical methods of statistical thermodynamics to compute these two thermodynamic properties, and this computational level is moderate. When the enthalpy of formation is calculated for those compounds, the results by method 1 differ from the experimental values. The absolute deviations are from 23.5 to 59.6 kJ‚mol-1, and the average deviation is 41.3 kJ‚mol-1. The reason is that the model chemistry (B3LYP/6-31G(d))

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Journal of Chemical and Engineering Data, Vol. 48, No. 3, 2003

Chart 1

Table 3. Valuesa of Group Additivity Contributions to the Enthalpy of Formation of PBDDs group ∆H°f/kJ‚mol-1 a

correction

CbH

CbBr

Cb-(O)

O-(Cb)2

∆ring

∆ortho

∆gauche

∆cis

13.807

44.769

-3.766

-78.659

8.368

3.138

8.368

-1.255

CHETAH 7.3, 2002 (ref 21).

employed due to the tradeoff of accuracy and cost is not accurate enough for the absolute internal energy calculation. The enthalpy of formation values calculated using method 2 are in good agreement with the experimental data of reference compounds. The average absolute deviation from experimental values by method 2 is 4.8 kJ‚mol-1, and the largest absolute deviation is 20.3 kJ‚mol-1. The predicted values using method 3 are also in reasonable agreement with the experimental data. The average absolute deviation from experimental values for method 3 is 9.8 kJ‚mol-1, and the largest absolute deviation is 27.0 kJ‚mol-1. Table 4 shows that the deviations in predicting the enthalpies of formation of 2,4,6-tribromoaniline and 2,4,6tribromophenol by method 2 are larger than those of the other compounds by the same method. Allot and Finch25 reported the experimental enthalpies of formation: (159.0 ( 2.6) kJ‚mol-1 for 2,4,6-C6H2Br3NH2 and (-0.9 ( 2.5) kJ‚mol-1 for 2,4,6-C6H2Br3OH; at the same time, they gave the estimated ∆fH°: (155.5 ( 12.5) kJ‚mol-1 for 2,4,6-C6H2Br3NH2 and (-28.0 ( 12.5) kJ‚mol-1 for 2,4,6-C6H2Br3OH using the Cox scheme.31 The estimated value for 2,4,6-C6H2Br3OH by Allot and Finch is close to the value by this study

but differs from the experimental value. Unfortunately, only one experimental value is available. For predictions of the enthalpies of formation of 2,4,6C6H2Br3NH2 and 2,4,6-C6H2Br3OH, the absolute deviations by method 3 are 27.0 kJ‚mol-1 and 3.7 kJ‚mol-1, respectively. Method 3 assumes that each substitution of Br for H on the benzene ring produces an increment of 7.4 kcal‚mol-1 (31.0 kJ‚mol-1) in ∆fH°. However, the experimental data show that the energy increment per Br substitution is 31.8 kJ‚mol-1 for 2,4,6-C6H2Br3OH and 24.0 kJ‚mol-1 for 2,4,6-C6H2Br3NH2, although the only difference between the two compounds is an NH2 versus an OH group. The results show that the traditional Benson’s method of group additivity (method 3) is still one of the most accurate methods for estimating formation enthalpy, and the calculation process is very simple and fast. However, Benson’s method can only give a very rough correction for cis-trans isomerization empirically. In estimating the enthalpies of isomers, method 2 is superior to Benson’s method, although methods 1 and 2 are far more computationally expensive. Compared with the selected experimental data, method 2 has the smallest absolute deviation among the three

Journal of Chemical and Engineering Data, Vol. 48, No. 3, 2003 731 Table 4. Comparison between Calculated Thermodynamic Parameters and Reference Data in the Gas Phase at 298.15 K and 101.325 kPa Cp/J‚mol-1‚K-1

S°/J‚mol-1‚K-1

compound

formula

U/hartree

H/hartree

G/hartree

calcd

ref

calcd

ref

benzene bromobenzene 1,2-dibromobenzene 1,3-dibromobenzene 1,4-dibromobenzene benzoic acid 2-bromobenzoic acid 3-bromobenzoic acid 4-bromobenzoic acid aniline 2,4,6-tribromoaniline phenol 2,4,6-tribromophenol naphthalene 1-bromonaphthalene 2-bromonaphthalene

C6H6 C6H5Br 1,2-C6H4Br2 1,3-C6H4Br2 1,4-C6H4Br2 C6H5COOH 2-C6H4BrCOOH 3-C6H4BrCOOH 4-C6H4BrCOOH C6H5NH2 2,4,6-C6H2Br3NH2 C6H5OH 2,4,6-C6H2Br3OH C10H8 1-C10H7Br 2-C10H7Br

-232.145 411 -2803.258 8485 -5374.368 5004 -5374.370 8092 -5374.370 8251 -420.701 2583 -2991.805 0285 -2991.813 1838 -2991.814 0273 -287.480 1316 -8000.822 1527 -307.356 5143 -8020.693 0940 -385.740 8631 -2956.853 7649 -2956.854 1686

-232.144 467 -2803.257 9045 -5374.367 5564 -5374.369 8652 -5374.369 8801 -420.700 3143 -2991.804 0665 -2991.812 2398 -2991.813 0833 -287.479 1866 -8000.821 2087 -307.355 5703 -8020.692 1500 -385.739 9181 -2956.852 8209 -2956.853 2246

-232.175 017 -2803.294 9035 -5374.408 9934 -5374.411 5972 -5374.410 9691 -420.740 5733 -2991.850 8085 -2991.857 2338 -2991.858 0373 -287.514 2136 -8000.869 8097 -307.391 1383 -8020.741 4250 -385.777 7621 -2956.896 5459 -2956.897 1446

81.8 99.3 116.2 116.8 116.6 124.4 141.7 141.8 141.9 102.6 152.7 101.5 151.8 131.7 148.8 149.2

82.53a

269.0 325.8 364.9 367.9 361.8 354.5 411.6 396.2 395.9 308.4 428.0 313.2 433.9 333.3 385.0 386.8

269.31a

∆fH°/kJ‚mol-1

deviation/kJ‚mol-1

compound

method 1

method 2

method 3

ref value

benzene bromobenzene 1,2-dibromobenzene 1,3-dibromobenzene 1,4-dibromobenzene benzoic acid 2-bromobenzoic acid 3-bromobenzoic acid 4-bromobenzoic acid aniline 2,4,6-tribromoaniline phenol 2,4,6-tribromophenol naphthalene 1-bromonaphthalene 2-bromonaphthalene

109.5 131.5 163.5 157.4 157.4 -240.1 -192.7 -214.1 -216.3 131.5 193.0 -43.1 32.7 197.4 220.8 219.7

82.9d 104.4 136.4 130.4 130.3 -294.1e -248.6 -270.1 -272.3 87.0f 147.9 -96.4g -21.2 150.6h 173.8 172.7

82.9c 105.0c 139.1 125.5c 134.7 -290.2c -256.7 -259.2 -262.6 86.9c 186.0 -96.4c 2.8 150.8c 181.5 181.5

82.93 ( 0.50 105.4 ( 4.1 133.9 ( 8.4 133.9 ( 8.4 126.4 ( 8.4 -294.1 ( 2.2 -246.9 ( 2.1 -268.3 ( 1.5 -275.9 ( 1.4 87.03 ( 0.88 159.0 ( 2.6 -96.36 ( 0.59 -0.9 ( 2.5 150.6 ( 1.1 174.3 ( 5.6 175.6 ( 2.3

reference 18 19 22 22 22 19 23 23 23 24 25 26 25 27 28 28

103.60a 133.02b

∆fG°/kJ‚mol-1

method method method method method method 1 2 3 1 2 3 26.6 26.1 29.6 23.5 31.0 54.0 54.2 54.2 59.6 44.5 34.0 53.3 33.6 46.8 46.5 44.1

-1.0 2.5 -3.5 3.9

5.2 -8.4 8.3

-1.7 -1.8 3.6

-9.8 9.1 13.3

-11.1

27.0

-20.3

3.7

-0.5 -2.9

7.2 5.9

156.5 164.7 188.2 181.3 183.1 -155.8 -122.1 -139.0 -141.1 214.8 250.3 53.5 70.7 271.0 282.1 280.6

129.9 137.6 161.2 154.2 156.0 -211.5 -178.1 -194.9 -197.1 152.8 199.3 -32.0 16.8 224.2 235.2 233.6

a Barin, 1989 (ref 29). b Thermodynamics Research Center, 1997 (ref 30). c Experimental values, CHETAH 7.3, 2002 (ref 21). 18. e Reference 19. f Reference 24. g Reference 26. h Reference 27.

methods under the condition of B3LYP/6-31G(d). As indicated by Foresman and Frisch,3 model chemistries that are known to be quite reliable for optimizing geometries can be quite poor at predicting absolute thermochemical properties, but such methods could be quite accurate at predicting other molecular properties, vibrational frequencies, and a variety of relative energy values: energy differences to similar molecules, reaction energies, and so on. The main reason method 2 can offer more accurate results is that the systematic errors in the method often cancel out across the systems being compared. Another reason is due to its use of experimental values as benchmarks.

315.71a

d

129.9 138.2 163.9 149.4 160.4 -205.9 -186.2 -184.1 -187.4 152.6 225.8 -32.0 40.8 223.8 242.9 242.4 Reference

The enthalpy of formation results of PBDDs predicted by method 1 are always much higher than those by method 2. The differences between the two methods are from 60 to 67 kJ‚mol-1. Because of the lack of experimental data, the corrections for cis-trans isomerization used in method 3 are very rough, and the level sequence of energies of isomers is different from that predicted by method 1 and method 2. Using free energy of formation values calculated by method 2, Figures 1-5 show clearly the differences among isomers.

As the substitute number of bromine increases, both the heat capacity and the absolute entropy of gaseous PBDDs increase.

Among 22 isomers of tetrabromodibenzo-p-dioxins, the Gibbs energies of 1,3,6,8-tetrabromodibenzo-p-dioxin (1,3,6,8TeBDD), 1,3,7,8-tetrabromodibenzo-p-dioxin (1,3,7,8-TeBDD), 1,3,7,9-tetrabromodibenzo-p-dioxin (1,3,7,9-TeBDD), and 2,3,7,8-tetrabromodibenzo-p-dioxin (TBDD, the most toxic compound in PBDDs) are lower than those of the other 18 isomers (see Figure 3). This means that these 4 isomers are more stable and easier to form during the formation process.

For predicting enthalpies of formation of PBDDs, the values obtained by method 2 and method 3 are in good agreement, except heptabromodibenzo-p-dioxins and octabromodibenzo-p-dioxin. As the substitution number of bromine increases, the enthalpies of formation by the three methods increase. The values of Gibbs energy of formation thus have the same tendency.

In the same way, 2,7-DiBDD and 2,8-DiBDD are easier to form than the other 8 isomers of dibromodibenzo-pdioxins. 1,3,7-TrBDD, 1,3,8-TrBDD, and 2,3,7-TrBDD are easier to form than the other 11 isomers of tribromodibenzo-p-dioxins. For the isomers of pentabromodibenzop-dioxins, 1,2,4,6,8-PeDBB, 1,2,4,7,8-PeDBB, and 1,2,4,7,9PeDBB are easier to form than the others. For the isomers

3.2. Calculation Results of the Thermodynamic Properties of PBDDs. The calculation results of U, G, H, S, Cp, ∆fH, and ∆fG for all the 76 PBDDs in the gas phase at 298.15 K and 101.325 kPa are listed in Table 5.

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Table 5. Thermodynamic Data of Gaseous PBDDs at 298.15 K and 101.325 kPa ∆fH°/kJ‚mol-1 compound

U/hartree

H/hartree

G/hartree

DD 1-MoBDD 2-MoBDD 1,2-DiBDD 1,3-DiBDD 1,4-DiBDD 1,6-DiBDD 1,7-DiBDD 1,8-DiBDD 1,9-DiBDD 2,3-DiBDD 2,7-DiBDD 2,8-DiBDD 1,2,3-TrBDD 1,2,4-TrBDD 1,2,6-TrBDD 1,2,7-TrBDD 1,2,8-TrBDD 1,2,9-TrBDD 1,3,6-TrBDD 1,3,7-TrBDD 1,3,8-TrBDD 1,3,9-TrBDD 1,4,6-TrBDD 1,4,7-TrBDD 2,3,6-TrBDD 2,3,7-TrBDD 1,2,3,4-TeBDD 1,2,3,6-TeBDD 1,2,3,7-TeBDD 1,2,3,8-TeBDD 1,2,3,9-TeBDD 1,2,4,6-TeBDD 1,2,4,7-TeBDD 1,2,4,8-TeBDD 1,2,4,9-TeBDD 1,2,6,7-TeBDD 1,2,6,8-TeBDD 1,2,6,9-TeBDD 1,2,7,8-TeBDD 1,2,7,9-TeBDD 1,2,8,9-TeBDD 1,3,6,8-TeBDD 1,3,6,9-TeBDD 1,3,7,8-TeBDD 1,3,7,9-TeBDD 1,4,6,9-TeBDD 1,4,7,8-TeBDD 2,3,7,8-TeBDD 1,2,3,4,6-PeBDD 1,2,3,4,7-PeBDD 1,2,3,6,7-PeBDD 1,2,3,6,8-PeBDD 1,2,3,6,9-PeBDD 1,2,3,7,8-PeBDD 1,2,3,7,9-PeBDD 1,2,3,8,9-PeBDD 1,2,4,6,7-PeBDD 1,2,4,6,8-PeBDD 1,2,4,6,9- PeBDD 1,2,4,7,8-PeBDD 1,2,4,7,9-PeBDD 1,2,4,8,9-PeBDD 1,2,3,4,6,7-HxBDD 1,2,3,4,6,8-HxBDD 1,2,3,4,6,9-HxBDD 1,2,3,4,7,8-HxBDD 1,2,3,6,7,8-HxBDD 1,2,3,6,7,9-HxBDD 1,2,3,6,8,9-HxBDD 1,2,3,7,8,9-HxBDD 1,2,4,6,7,9-HxBDD 1,2,4,6,8,9-HxBDD 1,2,3,4,6,7,8-HpBDD 1,2,3,4,6,7,9-HpBDD 1,2,3,4,6,7,8,9-OBDD

-612.352 659 -3 183.462 327 -3 183.464 505 -5 754.571 009 -5 754.573 184 -5 754.571 270 -5 754.571 807 -5 754.573 852 -5 754.573 817 -5 754.571 278 -5 754.573 156 -5 754.575 993 -5 754.576 007 -8 325.678 510 -8 325.679 145 -8 325.680 208 -8 325.682 340 -8 325.682 210 -8 325.679 815 -8 325.682 193 -8 325.684 379 -8 325.684 292 -8 325.681 787 -8 325.679 909 -8 325.682 440 -8 325.682 216 -8 325.684 377 -10 896.783 290 -10 896.787 482 -10 896.789 561 -10 896.789 484 -10 896.787 117 -10 896.787 739 -10 896.790 122 -10 896.790 195 -10 896.787 698 -10 896.788 614 -10 896.790 488 -10 896.788 354 -10 896.790 525 -10 896.790 161 -10 896.788 188 -10 896.792 422 -10 896.790 219 -10 896.792 414 -10 896.792 098 -10 896.788 006 -10 896.790 554 -10 896.792 547 -13 467.891 841 -13 467.894 139 -13 467.895 714 -13 467.897 545 -13 467.895 365 -13 467.897 638 -13 467.897 185 -13 467.895 335 -13 467.896 010 -13 467.897 791 -13 467.895 718 -13 467.898 160 -13 467.897 823 -13 467.895 964 -16 038.999 967 -16 039.001 793 -16 038.999 784 -16 039.002 067 -16 039.002 587 -16 039.002 920 -16 039.002 903 -16 039.002 468 -16 039.003 335 -16 039.003 342 -18 610.106 890 -18 610.107 186 -21 181.211 102

-612.351 714 -3 183.461 383 -3 183.463 561 -5 754.570 065 -5 754.572 240 -5 754.570 326 -5 754.570 863 -5 754.572 908 -5 754.572 873 -5 754.570 334 -5 754.572 212 -5 754.575 049 -5 754.575 062 -8 325.677 566 -8 325.678 201 -8 325.679 264 -8 325.681 396 -8 325.681 266 -8 325.678 871 -8 325.681 249 -8 325.683 435 -8 325.683 347 -8 325.680 843 -8 325.678 965 -8 325.681 495 -8 325.681 272 -8 325.683 433 -10 896.782 346 -10 896.786 538 -10 896.788 617 -10 896.788 540 -10 896.786 173 -10 896.786 795 -10 896.789 178 -10 896.789 251 -10 896.786 754 -10 896.787 669 -10 896.789 543 -10 896.787 410 -10 896.789 580 -10 896.789 217 -10 896.787 243 -10 896.791 478 -10 896.789 275 -10 896.791 470 -10 896.791 154 -10 896.787 062 -10 896.789 610 -10 896.791 602 -13 467.890 897 -13 467.893 195 -13 467.894 770 -13 467.896 601 -13 467.894 421 -13 467.896 694 -13 467.896 241 -13 467.894 391 -13 467.895 066 -13 467.896 847 -13 467.894 774 -13 467.897 216 -13 467.896 879 -13 467.895 020 -16 038.999 023 -16 039.000 849 -16 038.998 840 -16 039.001 123 -16 039.001 643 -16 039.001 976 -16 039.001 958 -16 039.001 524 -16 039.002 391 -16 039.002 398 -18 610.105 946 -18 610.106 242 -21 181.210 158

-612.398 258 -3 183.512 553 -3 183.514 941 -5 754.625 846 -5 754.628 080 -5 754.626 124 -5 754.626 728 -5 754.628 857 -5 754.628 758 -5 754.626 199 -5 754.628 000 -5 754.631 045 -5 754.630 986 -8 325.737 613 -8 325.738 678 -8 325.739 630 -8 325.741 703 -8 325.741 808 -8 325.739 302 -8 325.741 928 -8 325.743 967 -8 325.744 018 -8 325.741 525 -8 325.739 622 -8 325.742 126 -8 325.741 631 -8 325.743 941 -10 896.846 897 -10 896.851 269 -10 896.853 409 -10 896.853 407 -10 896.851 076 -10 896.851 929 -10 896.854 328 -10 896.854 302 -10 896.851 970 -10 896.852 316 -10 896.854 561 -10 896.852 383 -10 896.854 333 -10 896.854 232 -10 896.852 072 -10 896.856 776 -10 896.854 573 -10 896.856 564 -10 896.856 403 -10 896.852 397 -10 896.854 642 -10 896.856 484 -13 467.960 070 -13 467.962 397 -13 467.963 863 -13 467.965 828 -13 467.963 901 -13 467.965 776 -13 467.965 861 -13 467.963 795 -13 467.964 797 -13 467.966 827 -13 467.964 421 -13 467.966 533 -13 467.966 567 -13 467.964 495 -16 039.072 715 -16 039.074 876 -16 039.072 614 -16 039.074 504 -16 039.075 172 -16 039.075 954 -16 039.075 878 -16 039.074 950 -16 039.076 437 -16 039.076 585 -18 610.183 989 -18 610.185 109 -21 181.292 768

a

Kolesov et al., 1998 (ref 16).

∆fG°/kJ‚mol-1

Cp/J‚ method method method method method method S°/J‚ 1 2 3 1 2 3 mol-1‚K-1 mol-1‚K-1 409.9 450.6 452.5 491.2 491.7 491.4 491.9 492.7 492.1 492.0 491.3 493.1 492.5 528.8 532.6 531.6 531.1 533.1 532.2 534.3 533.0 534.3 534.4 534.1 533.9 531.5 532.8 568.4 570.0 570.6 571.2 571.5 573.6 573.7 572.8 574.3 569.3 572.5 572.2 570.2 572.5 570.9 575.0 575.0 573.2 574.6 575.3 572.7 571.3 609.1 609.4 608.4 609.6 611.8 608.3 613.1 611.2 614.1 616.2 613.3 610.4 613.7 611.8 648.9 651.9 649.6 646.2 647.5 651.4 650.9 646.6 652.0 653.3 687.2 694.5 727.5

180.6 197.5 198.2 214.6 215.0 214.3 214.4 215.0 215.0 214.4 215.1 215.6 215.5 231.8 231.5 231.5 232.0 232.1 231.5 231.9 232.4 232.6 232.0 231.3 231.8 231.9 232.5 248.4 248.7 249.2 249.3 248.6 248.3 248.8 248.8 248.4 248.4 249.0 248.2 248.9 249.0 248.5 249.4 248.7 249.5 249.4 247.9 248.8 249.5 265.3 265.9 265.7 266.1 265.5 266.0 266.3 265.7 265.3 265.8 265.0 265.7 265.6 265.3 282.4 282.8 282.1 282.7 282.8 282.5 282.5 282.7 281.9 282.1 299.5 299.2 316.2

7.4 39.3 33.6 73.8 68.1 73.1 71.7 66.3 66.4 73.1 68.1 60.7 60.6 111.3 109.7 106.9 101.3 101.6 107.9 101.7 95.9 96.2 102.7 107.7 101.0 101.6 95.9 156.1 145.1 139.6 139.8 146.0 144.4 138.1 137.9 144.5 142.1 137.2 142.8 137.1 138.0 143.2 132.1 137.9 132.1 133.0 143.7 137.0 131.8 190.9 184.9 180.7 175.9 181.7 175.7 176.9 181.7 180.0 175.3 180.7 174.3 175.2 180.1 226.8 222.1 227.3 221.3 220.0 219.1 219.1 220.3 218.0 218.0 265.9 265.2 312.2

-59.2a -27.5 -33.3 6.7 1.0 6.0 4.6 -0.7 -0.6 6.0 1.1 -6.4 -6.4 44.1 42.4 39.6 34.0 34.4 40.7 34.4 28.7 28.9 35.5 40.4 33.8 34.4 28.7 88.6 77.6 72.1 72.3 78.5 76.9 70.7 70.5 77.0 74.6 69.7 75.3 69.6 70.6 75.7 64.6 70.4 64.6 65.5 76.2 69.5 64.3 123.2 117.2 113.0 108.2 113.9 108.0 109.2 114.0 112.3 107.6 113.0 106.6 107.5 112.4 158.9 154.1 159.4 153.4 152.0 151.2 151.2 152.4 150.1 150.1 197.8 197.0 243.8

-53.6 -22.6 -22.6 11.5 18.8 7.1 8.4 8.4 8.4 8.4 11.5 8.4 8.4 45.6 52.9 42.5 42.5 42.5 42.5 49.8 49.8 49.8 49.8 38.1 38.1 42.5 42.5 79.7 76.6 76.6 76.6 76.6 83.9 83.9 83.9 83.9 76.6 83.9 72.2 76.6 83.9 76.6 91.2 79.5 83.9 91.2 67.8 72.2 76.6 110.7 110.7 110.7 118.0 106.3 110.7 118.0 110.7 118.0 125.3 113.6 118.0 125.3 118.0 144.8 152.1 140.4 144.8 144.8 152.1 152.1 144.8 159.4 159.4 178.9 186.2 213.0

122.7 145.7 139.4 171.3 165.4 170.5 169.0 163.4 163.6 170.4 165.6 157.6 157.8 200.9 198.1 195.6 190.1 189.9 196.4 189.5 184.2 184.1 190.6 195.6 189.0 190.3 184.3 237.0 225.5 219.9 219.9 226.0 223.8 217.5 217.5 223.7 222.8 216.9 222.6 217.5 217.7 223.4 211.0 216.8 211.6 212.0 222.5 216.6 211.8 262.9 256.8 252.9 247.8 252.8 247.9 247.7 253.1 250.5 245.1 251.5 245.9 245.8 251.3 290.2 284.5 290.4 285.5 283.7 281.7 281.9 284.3 280.4 280.0 321.1 318.1 358.5

56.2 78.9 72.6 104.2 98.4 103.5 101.9 96.3 96.6 103.3 98.6 90.6 90.8 133.6 130.8 128.3 122.9 122.6 129.2 122.3 116.9 116.8 123.3 128.3 121.8 123.1 117.0 169.5 158.0 152.4 152.4 158.5 156.3 150.0 150.1 156.2 155.3 149.4 155.1 150.0 150.2 155.9 143.6 149.3 144.1 144.5 155.1 149.2 144.3 195.2 189.1 185.2 180.1 185.1 180.2 180.0 185.4 182.8 177.4 183.8 178.2 178.1 183.6 222.2 216.6 222.5 217.5 215.8 213.7 213.9 216.4 212.5 212.1 252.9 250.0 290.1

61.8 83.8 83.3 109.0 116.2 104.6 105.7 105.4 105.6 105.7 109.0 105.3 105.5 135.1 141.3 131.2 131.3 130.7 131.0 137.7 138.0 137.7 137.6 126.0 126.1 131.2 130.8 160.6 157.0 156.8 156.6 156.6 163.3 163.2 163.5 163.0 157.2 163.6 152.0 156.9 163.6 156.7 170.2 158.4 163.4 170.3 146.6 151.8 156.6 182.6 182.6 182.9 189.8 177.4 182.9 188.8 182.0 188.5 195.2 184.3 189.6 195.9 189.2 208.1 214.5 203.5 208.9 208.5 214.7 214.8 208.8 221.8 221.4 234.0 239.1 259.3

Journal of Chemical and Engineering Data, Vol. 48, No. 3, 2003 733

Figure 1. Comparison of Gibbs energies of formation of dibromodibenzo-p-dioxin isomers.

Figure 2. Comparison of Gibbs energies of formation of tribromodibenzo-p-dioxin isomers.

Figure 3. Comparison of Gibbs energies of formation of tetrabromodibenzo-p-dioxin isomers.

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Journal of Chemical and Engineering Data, Vol. 48, No. 3, 2003

Figure 4. Comparison of Gibbs energies of formation of pentabromodibenzo-p-dioxin isomers.

Figure 5. Comparison of Gibbs energies of formation of hexabromodibenzo-p-dioxin isomers.

of hexabromodibenzo-p-dioxins, 1,2,4,6,7,9-HxBDD and 1,2,4,6,8,9-HxBDD are easier to form than the others.

compound 2,3,7,8-TeBDD are more stable than the others and easier to form during the formation process.

4. Conclusion

Acknowledgment

(1) Under the computing level of B3LYP/6-31G(d), method 2 has the smallest average absolute deviation and maximum absolute deviation, (4.8 and 20.3) kJ‚mol-1, from the experimental values of formation enthalpy of the reference compounds, and method 2 is simpler than method 1. (2) Benson’s method is still an accurate method for estimating thermodynamic properties, and calculation procedures are very simple and much faster than methods 1 and 2. But this method can only give much rougher corrections for cis-trans isomerization empirically. Method 2 is superior to Benson’s method in predicting the formation enthalpies of isomers. (3) All the heat capacity, entropy, enthalpy, and Gibbs energy of formation values for the 76 PBDDs increase as the substitute number of bromine increases. The values of enthalpy and Gibbs energy of formation of PBDDs calculated by method 2 are recommended. (4) For isomers of tetrabromodibenzo-p-dioxins, 1,3,6,8TeBDD, 1,3,7,8-TeBDD, 1,3,7,9-TeBDD, and the most toxic

Helpful advice from Mr. Douglas J. Fox, Gaussian Inc., is acknowledged. Literature Cited (1) Polybrominated Dibenzo-p-dioxins and Dibenzofurans; Environmental Health Criteria 205; World Health Organization: Geneva, 1998. (2) Frisch, Æ.; Frisch, M. J. Gaussian 98 User’s Reference, 2nd ed.; Gaussian, Inc.: Pittsburgh, 1999. (3) Foresman, J. B.; Frisch Æ. Exploring Chemistry with Electronic Structure Methods, 2nd ed.; Gaussian, Inc.: Pittsburgh, 1996. (4) Koester, C. J.; Hites, R. A. Calculated physical properties of polychlorinated dibenzo-p-dioxins and dibenzofurans. Chemosphere 1988, 17, 2355-2362. (5) Huang, C. L.; Harrison, B. K.; Madura, J.; Dolfing, J. Gibbs free energies of formation of PCDDs: evaluation of estimation methods and application for predicting dehalogenation pathways. Environ. Toxicol. Chem. 1996, 15, 824-836. (6) Saito, N.; Fuwa, A. Prediction for thermodynamic function of dioxins for gas phase using semi-empirical molecular orbital method with PM3 Hamiltonian. Chemosphere 2000, 40, 131-145. (7) McQuarrie, D. A.; Simon, J. D. Molecular Thermodynamics; University Science Books: Sausalito, CA, 1999.

Journal of Chemical and Engineering Data, Vol. 48, No. 3, 2003 735 (8) Hehre, W. J.; Radom, L.; Schleyer, P. v. R.; Pople, J. A. Ab Initio Molecular Orbital Theory; Wiley: New York, 1986. (9) Ochterski, J. W. Thermochemistry in Gaussian; http://www. gaussian.com/ thermo/thermo.pdf, 2000. (10) Curtiss, L. A.; Raghavachari, K.; Deutsch, P. W.; Pople, J. A. Theoretical study of Si2Hn (n ) 0-6) and Si2Hn+ (n ) 0-7): appearance potentials, ionization potentials, and enthalpies of formation. J. Chem. Phys. 1991, 95, 2433-2444. (11) Curtiss, L. A.; Raghavachari, K.; Redfern, P. C.; Pople, J. A. Assessment of Gaussian-2 and density functional theory. J. Chem. Phys. 1997, 106, 1063-1079. (12) Dixon, D. A.; Jong, W. A. de; Peterson, K. A.; Francisco, J. S. Heats of Formation of CBr, CHBr, and CBr2 from Ab Initio Quantum Chemistry. J. Phys. Chem. A 2002, 106, 4725-4728. (13) Feller, D.; Peterson, K. A.; Jong, W. A. de; Dixon, D. A. Performance of Coupled Cluster Theory in Thermochemical Calculations of Small Halogenated Compounds. J. Chem. Phys. 2003, 118, 3510-3522. (14) Moore, C. E. Atomic Energy Levels; U.S. National Bureau of Standards Circular 467; U.S. National Bureau of Standards: Washington, DC, 1949. (15) Chase, M. W. NIST-JANAF Thermochemical Tables, 4th ed.; Journal of Physical and Chemical Reference Data Monograph No. 9; American Institute of Physics: Woodbury, NY, 1998. (16) Kolesov, V. P.; Dorofeeva, O. V.; Iorish, V. S.; Papina, T. S.; Luckyanova, V. A.; Melkhanova, S. V. Experimental measurements and group additivity approach for estimating the standard molar enthalpies of formation of dioxins. Organohalogen Compd. 1998, 36, 201-204. (17) Ferguson, K. C.; Okafo, E. N.; Whittle, E. Bond dissociation energies from equilibrium studies. Part 4. The equilibrium Br2 + CH4 ) HBr + CH3Br. Determination of D(CH3-Br) and ∆Hf°(CH3Br,g). J. Chem. Soc., Faraday Trans. 1 1973, 69, 295301. (18) Prosen, E. J.; Johnson, W. H.; Rossini, F. D. Heats of combustion and formation at 25 °C of the alkylbenzenes through C10H14, and of the higher normal monoalkylbenzenes. J. Res. Natl. Bur. Stand. (U.S.) 1946, 36, 455-461. (19) Pedley, J. B.; Naylor, R. D.; Kirby, S. P. Thermochemical Data of Organic Compounds, 2nd ed.; Chapman and Hall: London, 1986.

(20) Benson, S. W. Thermochemical Kinetics, 2nd ed.; John Wiley & Sons: New York, 1976. (21) The ASTM Computer Program for Chemical Thermodynamic and Energy Release Evaluation - CHETAH 7.3 User’s Guide; ASTM International: West Conshohocken, PA, Jan 2002. (22) Olesik, S.; Baer, T.; Morrow, J. C. Dissociation rate of energyselected dichloro- and dibromobenzene ions. J. Phys. Chem. 1986, 90, 3563-3568. (23) Sabbah, R.; Rojas Aguilar, A. Thermodynamic study of the three isomers of bromo and iodobenzoic acids, Part II. Struct. Chem. 1996, 7, 383-390. (24) Hatton, W. E.; Hildenbrand, D. L.; Sinke, G. C.; Stull, D. R. Chemical thermodynamic properties of aniline. J. Chem. Eng. Data 1962, 7, 229-231. (25) Allot, P. H.; Finch, A. Enthalpies of formation of 2,4,6-tribromophenol and of 2,4,6-tribromoaniline. J. Chem. Thermodyn. 1987, 19, 771-779. (26) Cox, J. D. The heats of combustion of phenol and the three cresols. Pure Appl. Chem. 1961, 2, 125-128. (27) Coleman, D. J.; Pilcher, G. Heats of combustion of biphenyl, bibenzyl, naphthalene, anthracene, and phenanthrene. Trans. Faraday Soc. 1966, 62, 821-827. (28) Ribeiro da Silva, M. A. V.; Ferrao, M. L. C. C. H.; Lopes, A. J. M. Enthalpies of combustion of each of the two bromonaphthalenes. J. Chem. Thermodyn. 1993, 25, 229-235. (29) Barin, I. Thermochemical Data of Pure Substances; VCH, Verlags Gesellschaft: Weinheim, 1989. (30) Thermodynamics Research Center. Selected Values of Properties of Chemical Compounds; Texas A&M University: College Station, TX, 1997. (31) Cox, J. D. A method of estimating the enthalpies of formation of benzene derivatives in the gas state. NPL Report CHEM 83, June 1978. Received for review December 18, 2002. Accepted March 19, 2003. This work was financially supported by a Grant-in-Aid from the Ministry of Environment, Japan.

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